Q6. Which of the following statements is correct about Kepler’s laws?

Q7. What ensures that the area swept by a planet’s orbit is constant over equal time intervals?

• A. Constant speed
• B. Conservation of angular momentum
• C. Elliptical orbit shape
• D. Conservation of energy

Q8. A \( 1000 \, \text{kg} \) satellite orbits Earth at \( 1.5 R_E \) from the center. What is its potential energy? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

• A. -4.0 × 10¹⁰ J
• B. -4.2 × 10¹⁰ J
• C. -4.5 × 10¹⁰ J
• D. -4.7 × 10¹⁰ J

Q9. At what depth below Earth’s surface is \( g \) reduced to \( 5.39 \, \text{m/s}^2 \)? (\( g_0 = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

• A. 2.8 × 10⁶ m
• B. 2.9 × 10⁶ m
• C. 3.0 × 10⁶ m
• D. 3.1 × 10⁶ m

Q10. A satellite orbits a planet at \( 2 \times 10^6 \, \text{m} \) from its center with a period of 2 hours. What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

• A. 8.5 × 10²² kg
• B. 9.0 × 10²² kg
• C. 9.1 × 10²² kg
• D. 9.5 × 10²² kg

Q11. What is the minimum speed to escape from \( 6 R_E \) from Earth’s center? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

• A. 4.5 km/s
• B. 4.6 km/s
• C. 4.7 km/s
• D. 4.8 km/s

Q12. Why does the Moon have no atmosphere compared to Earth?

• A. It has no magnetic field
• B. Its escape speed is low
• C. It is closer to the Sun
• D. It has no gravitational force

Q13. A satellite orbits Earth at \( 15 R_E \) from the center. What is its orbital speed? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

• A. 2.0 × 10³ m/s
• B. 2.1 × 10³ m/s
• C. 2.2 × 10³ m/s
• D. 2.3 × 10³ m/s

Q14. A \( 3 \, \text{kg} \) mass is moved from \( 4 R_E \) to \( 8 R_E \) from Earth’s center. What is the change in potential energy? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

• A. 2.2 × 10⁷ J
• B. 2.3 × 10⁷ J
• C. 2.4 × 10⁷ J
• D. 2.5 × 10⁷ J

Q15. What happens to a satellite’s orbital speed if its altitude increases?

• A. It increases
• B. It decreases
• C. It remains constant
• D. It becomes zero